$11^{1}_{61}$ - Minimal pinning sets
Pinning sets for 11^1_61 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_61 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 128
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.89692
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 5, 10}
4
[2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.0
5
0
0
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,6,6,7],[0,7,7,8],[0,8,8,5],[1,4,6,1],[1,5,2,2],[2,8,3,3],[3,7,4,4]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[15,8,16,9],[17,12,18,13],[10,4,11,3],[1,6,2,7],[7,14,8,15],[16,14,17,13],[11,4,12,5],[5,2,6,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (3,18,-4,-1)(1,8,-2,-9)(9,2,-10,-3)(17,4,-18,-5)(13,6,-14,-7)(15,10,-16,-11)(11,14,-12,-15)(5,12,-6,-13)(7,16,-8,-17)
Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)(-11,11)(-12,12)(-13,13)(-14,14)(-15,15)(-16,16)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-9,-3)(-2,9)(-4,17,-8,1)(-5,-13,-7,-17)(-6,13)(-10,15,-12,5,-18,3)(-11,-15)(-14,11,-16,7)(2,8,16,10)(4,18)(6,12,14)
Loop annotated with half-edges
11^1_61 annotated with half-edges